Visualizing Returns


Kerry Back

BUSI 721, Fall 2022
JGSB, Rice University

Let’s look at the history of stock market returns – either the U.S. market as a whole or individual stocks or funds.

Four different plots

  • scatter plot of returns by year
  • box plot of annual returns
  • accumulations \((1+r_1)(1+r_2) \cdots (1+r_n)\) by \(n\)
  • accumulations with log scale

Box Plot

  • Box contains 25th percentile through 75th percentile

  • Median is indicated as a line in the box

  • Fences extend 1.5 times inter-quartile range from 25th and 75th percentiles or to the most extreme observation if that is closer to the box

    • inter-quartile range = 75th minus 25th percentile)

  • Points outside the fences are outliers

    • if you simulate data from a normal distribution, there will typically be very few points outside the fences

HTML tutorial

Why log plots? An Example

  • Let’s look at accumulations from two hypothetical stocks.
    • stock 1: 10% per year
    • stock 1: 2% per year until 2000 and 10% afterwards
  • It will appear that stock 2 did nothing before 2000 and earned a lot less than stock 1 even after 2000.

Plot of the Example

Log (base 10) of accumulation

Map \(y\) tick labels to dollars

HTML tutorial